CPM Homework Help : ACC7 Problem 9-33

Based on the given information, determine which pairs of lines, if any, are parallel. If none are necessarily parallel, write “none.”

Hint:

Alternate interior angles and corresponding angles are equal only if the lines cut by the transversal are parallel.
Conversely, if the angles are equal the lines must be parallel. $\rightarrow$ . Alternate interior angles and corresponding angles have equal measure only if the lines cut by the transversal are parallel.
Conversely, if the angle measures are equal, the lines must be parallel.

$m∠2 = m∠7$
Hint (a):
These are alternate interior angles.
$m∠3 = m∠11$
Hint (b):
These are corresponding angles.
Answer (b):
$e$ and $f$
$m∠1 = m∠12$
Hint (c):
In the diagram below, the measures of $\angle$ 1 and $\angle$ 12 are equal. Do any two lines look parallel?
$m∠13 = m∠12$
Hint (d):
Vertical angles are always equal. $\rightarrow$ Vertical angles always have equal measure.
Answer (d):
$c$ and $d$
$∠6$ and $∠7$ are supplementary.
Hint (e):
Angle 6 would be supplementary to angle 7 if angle 7 was equal to angle 2. $\rightarrow$ $\angle6$ would be supplementary to $\angle7$ if m $\angle7$ was equal to m $\angle2$ .

Two increasing transversal lines, c, and d, cross two horizontal lines, e, and f, creating 4 points of intersection. The angles at each intersection are labeled, starting at the top left and going clockwise as follows: Intersection of c, and e: 1, 2, 6, and 5. Intersection of, d, and e: 3, 4, 8, and 7. Intersection of c, and f: 9, 10, 14, and 13. Intersection of, d, and f: 11, 12, 16, and 15.